Question
(12x^5+4x^4+9x^3-10x^2+15)-(24x^5+9x^3-7x^2+8)
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Answered by
GPT-4o mini
To simplify the expression \( (12x^5 + 4x^4 + 9x^3 - 10x^2 + 15) - (24x^5 + 9x^3 - 7x^2 + 8) \), we'll distribute the negative sign through the second set of parentheses and then combine like terms.
1. Distributing the negative sign:
\[
12x^5 + 4x^4 + 9x^3 - 10x^2 + 15 - 24x^5 - 9x^3 + 7x^2 - 8
\]
2. Now we'll group the like terms:
- \( x^5 \) terms: \( 12x^5 - 24x^5 = -12x^5 \)
- \( x^4 \) terms: \( 4x^4 \) (only one term)
- \( x^3 \) terms: \( 9x^3 - 9x^3 = 0 \) (they cancel out)
- \( x^2 \) terms: \( -10x^2 + 7x^2 = -3x^2 \)
- Constant terms: \( 15 - 8 = 7 \)
3. Combining all the results:
\[
-12x^5 + 4x^4 - 3x^2 + 7
\]
Thus, the simplified expression is:
\[
\boxed{-12x^5 + 4x^4 - 3x^2 + 7}
\]
1. Distributing the negative sign:
\[
12x^5 + 4x^4 + 9x^3 - 10x^2 + 15 - 24x^5 - 9x^3 + 7x^2 - 8
\]
2. Now we'll group the like terms:
- \( x^5 \) terms: \( 12x^5 - 24x^5 = -12x^5 \)
- \( x^4 \) terms: \( 4x^4 \) (only one term)
- \( x^3 \) terms: \( 9x^3 - 9x^3 = 0 \) (they cancel out)
- \( x^2 \) terms: \( -10x^2 + 7x^2 = -3x^2 \)
- Constant terms: \( 15 - 8 = 7 \)
3. Combining all the results:
\[
-12x^5 + 4x^4 - 3x^2 + 7
\]
Thus, the simplified expression is:
\[
\boxed{-12x^5 + 4x^4 - 3x^2 + 7}
\]
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